February/March_AMP

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M A T E R I A L S

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easurement of grain size and

distribution can be performed

using bothmanual (ASTM E112)

and image analysis (E1382) methods.

Standard E112 is designed to measure

grain size in specimens with equiaxed

grains and a unimodal (normal), or

Gaussian, grain size distribution. How-

ever, it does not define how to deter-

mine if grains in a specimen adhere to

this criterion. This article demonstrates

how to evaluate grain size distribution,

which can be done using either grain-

area or intercept-lengthmeasurements.

The use of grain areas to evaluate distri-

bution is preferred, as the amount of

data per field is less, and the calculation

of ASTM grain size, G, is a simple and

direct matter. Further, the relationship

between mean lineal intercept length

and grain size is empirical.

Grain structures of some metal

specimens have grain distributions

other than unimodal or Gaussian dis-

tribution. For example, high-alloy and

stainless steels and nickel-base superal-

loys commonly have bimodal grain size

distributions in the as-rolled and solu-

tion annealed condition—especially if

the annealing temperature is below the

recommended temperature. A range of

distributions can exist between speci-

mens that exhibit unimodal Gaussian

distributions and those that clearly ex-

hibit bimodal, or duplex, grain size dis-

tributions. Because the nature of grain

size distribution can influence mechan-

ical properties and service behavior, it

is important to accurately characterize

this parameter. The best way to evalu-

ate grain size distribution is to measure

grain areas and plot the percentage of

grain areas per ASTM G class versus

ASTM grain size number (G), while cal-

culating the skew and kurtosis (sharp-

ness of the peak of a frequency-distri-

bution curve) of the measured grain

areas. A kurtosis of 3 represents a per-

fect unimodal, or Gaussian, grain size

distribution, while values of >5 indicate

non-Gaussian distributions.

ANALYTICAL PROCEDURE

Grain areas can be measured using

image analysis (IA) and electron back-

scatter diffraction (EBSD). A reasonably

large number of grains (typically, at least

500 grains) must be measured using

randomly selected fields; both methods

required excellent metallographic spec-

imen preparation. For IA, grain structure

must be fully revealed with minimal

missing grain edges between adjacent

grains, although this technique can

correct for some missing grain bound-

aries. EBSD requires a specimen with

excellent flatness and freedom from de-

formation-induced subsurface damage,

which reduces the percentage of pixels

that generate diffraction patterns that

can be indexed. If a face-centered-cu-

bic metal specimen exhibits annealing

twins, they must be suppressed by the

etchant used, removed by the image

analysis program, or removed by the

orientation differences across the twin

boundary by EBSD.

To define a normal distribution,

plot the area percentage of grains per

ASTM grain size class. The definition of

G according to E112 is:

= 2

G-1

(1)

where N

is the number of grains per

square inch at a magnification of 100×

and G is the ASTM grain size number.

Skew and kurtosis are calculated from

ANALYSIS OF GRAINSIZE

DISTRIBUTIONS

Because the nature of grain size distribution can influence mechanical properties and

service behavior, it is important to accurately characterize this parameter.

George F. Vander Voort, FASM,* Struers Inc. (Consultant), Cleveland

the raw measurement data of the grain

areas. Calculate the kurtosis of the data

using an application such as Microsoft

Excel. Next, order grain areas from larg-

est to smallest, then add up grain areas

according to how they relate to specific

ASTM G values as shown in Table 1. In

the table, for a given G class, areas are

binned according to the area for a given

G value plus or minus the area for G-0.5

to G+0.5. Total grain areas for each G

value are summed and divided by the

total areas of all measured grains and

expressed as a percentage.

ANALYSIS EXAMPLES

Example 1.

Figure 1 shows the

microstructure of a motor lamination

steel with a very low carbon content,

ASTM G A max,

A min,

TABLE 1—BINNING OF GRAIN AREAS

BY ASTM G CLASS

365,008

182,504

91,239

45,620

22,810

11,405

5703

2851

1426

713

356

178

89.5

44.6

22.3

11.1

5.57

2.79

*Member of ASM International